EUDML

Let $𝒴$ be a smooth compact oriented riemannian manifoldwithout boundary, and assume that its $1$ -homology group has notorsion. Weak limits of graphs of smooth maps $u_{k} : B^{n} \to 𝒴$ with equibounded total variation give riseto equivalence classes of cartesian currents in ${cart}^{1, 1} (B^{n} 𝒴)$ for which we introduce a natural $B V$ -energy.Assume moreover that the first homotopy group of $𝒴$ iscommutative. In any dimension $n$ we prove that every element $T$ in ${cart}^{1, 1} (B^{n} 𝒴)$ can be approximatedweakly in the sense of currents by a sequence of graphs...

The singular set of the minima of certain quadratic functionals

Mariano Giaquinta; Enrico Giusti — 1984

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Weak and strong density results for the Dirichlet energy

Mariano Giaquinta; Domenico Mucci — 2004

Journal of the European Mathematical Society

Let $𝒴$ be a smooth oriented Riemannian manifold which is compact, connected, without boundary and with second homology group without torsion. In this paper we characterize the sequential weak closure of smooth graphs in $B^{n} \times 𝒴$ with equibounded Dirichlet energies, $B^{n}$ being the unit ball in $ℝ^{n}$ . More precisely, weak limits of graphs of smooth maps $u_{k} : B^{n} \to 𝒴$ with equibounded Dirichlet integral give rise to elements of the space ${cart}^{2, 1} (B^{n} \times 𝒴)$ (cf. [4], [5], [6]). In this paper we prove that every element $T$ in ${cart}^{2, 1} (B^{n} \times 𝒴)$ is the weak limit...

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Remarks on the Regularity of Weak Solutions to Some Variational Inequalities.

On the Dirichlet Probelm for Surfaces of Prescribed Mean Curvature.

A Counter-Example to the Boundary Regularity of Solutions to Elliptic Quasilinear Systems.

David Hilbert a variační počet

On the Partial Regularity of Weak Solutions of Nonlinear Parabolic Systems.

Remarks on the regularity of the minimizers of certain degenerate functionals

The Dirichlet Energy of Mappings with values into the sphere.

Almost-Everywhere Regularity Results for Solutions of Non Linear Elliptic Systems.

Differentiability of Minima of Non-Differentiable Functionals.

Caccioppoli's Inequality and Legendre-Hadamard Condition.

A priori estimates for harmonic mappings.

Partial regularity of minimizers of quasiconvex integrals

Quasi-minima

The BV-energy of maps into a manifold : relaxation and density results

The singular set of the minima of certain quadratic functionals

Weak and strong density results for the Dirichlet energy

On the regularity of weak solutions to nonlinear elliptic systems via Liouville's type property

Connectivity properties of the range of a weak diffeomorphism

Functionals with linear growth in the calculus of variations. I.

Functionals with linear growth in the calculus of variations. II.